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Full text of "Mathematical And Physical Papers - Iii"

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diction with the law of continuity. For the sake of illustration, let us consider the phenomenon of total internal reflexion. Let P be a point in air situated at the distance z from an infinite plane separating air from glass. Conceive light having an intensity equal to unity, and coming from an infinitely distant point, to be incident internally on this plane at an angle 7 -f 0, where 7 is the angle of total internal reflexion. The intensity at P is commonly, and for most purposes correctly, considered as altering abruptly with 6, having, so long as 6 is negative, a finite value which does not vanish with 9, but being equal to zero when 6 is positive. The mode in which the law of continuity is in this case obeyed is worthy of notice. In the analytical expression for the vibration, when 9 passes from negative to positive, the coordinate z passes from under a circular function into an exponential with a negative index, containing in its denominator X, the length of a wave of light. As 0 increases through zero, the expression for the vibration alters continuously; but if z be large compared with X it decreases with extreme rapidity when 6 becomes positive. On account of the excessive smallness of X, it is sufficient for most purposes to consider the intensity as a function of 6 which vanishes abruptly; and indeed it would be hardly correct to consider it otherwise. For the use of the term intensity implies that we are considering light as usual, whereas those phenomena which require us to take into account the disturbance in the second medium which exists when the angle of incidence exceeds that of total internal reflexion, lead us to consider the nature as well as the magnitude of that disturbance, which no longer consists of a series of plane waves constituting light as usual. It is in some similar sense that I mean to say that we may suppose the function /(#), which expresses the intensity of the truly dispersed light, to alter abruptly, without thereby implying any violation in the law of continuity. In observing by the fourth method, the portion of the spectrum operated on, though it may be small, is necessarily finite, and in some cases no separation could be made out between the beams of truly and falsely dispersed light. Hence I cannot undertake to say from observation, whether the variation of /(#) be always continuous, though sometimes very rapid, or be in some cases actually abrupt. I think, however, that observation rather favours the former supposition, a supposition which, independently {, j                           of observation, seems by far the more likely.
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